Konstantinos Spiliopoulos



Department of Mathematics and Statistics
Boston University
111 Cummington Street, Boston MA 02215

Office: MCS233D
Tel: +1-617-353-5209
e-mail: kspiliop_at_math.bu.edu
to send me an email replace _at_ by @.


[ Research Interests and Curriculum Vitae | Publications | Distinctions, Awards and Grants | Editorial work | Invited Talks and Conferences | Seminars | Teaching | Links]


Welcome! I am an Associate Professor at the Department of Mathematics and Statistics, Boston University. I am affiliated with the Center for Information and Systems Engineering, Boston University and I have been a junior faculty fellow at the Hariri Institute for Computing and Computational Sciences & Engineering at Boston University. I completed my PhD at the Department of Mathematics, University of Maryland at College Park, advised by Professor Mark Freidlin and I was at the Division of Applied Mathematics, Brown University as a Prager Assistant Professor from 2009-2012. My undergraduate studies were in Applied Mathematics and Physics at the National Technical University of Athens in Greece. (NTUA).


Research interests:

My research lies broadly in the areas of stochastic processes, algorithmic and computational methods in machine and statistical learning, applied mathematics and probability, financial mathematics, asymptotic problems for stochastic processes and partial differential equations such as multiscale methods and large deviations, statistical analysis and inference. In particular: top


Submitted papers:

  1. "PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence", (with Justin Sirignano and Jonathan MacArt), 2021, [ArXiv preprint], submitted.
  2. "Online Adjoint Methods for Optimization of PDEs", (with Justin Sirignano), 2021, [ArXiv preprint], submitted.
  3. "Moderate deviations for systems of slow-fast stochastic reaction-diffusion equations", (with Ioannis Gasteratos and Mickey Salins), 2021, [ArXiv preprint], submitted.
  4. "Large deviations for interacting multiscale particle systems", (with Zachary Bezemek), 2020, [ArXiv preprint], submitted.
  5. "Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models", (with Samuel A. Isaacson and Jingwei Ma), 2020, [ArXiv preprint], submitted.
  6. "Scaling Limit of Neural Networks with the Xavier Initialization and Convergence to a Global Minimum ", (with Justin Sirignano), 2019, [ArXiv preprint], unpublished technical note, available on arxiv.

Book Chapters:

  1. "Importance sampling for metastable and multiscale dynamical systems", Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, (Editors: D. Holcman) , Springer, 2017, pp 29-53, [ArXiv preprint]
  2. "Systemic Risk and Default Clustering for Large Financial Systems", Large Deviations and Asymptotic Methods in Finance, (Editors: P. Friz, J. Gatheral, A. Gulisashvili, A. Jacqier, J. Teichmann) , Springer Proceedings in Mathematics and Statistics, Vol. 110 2015, [SSRN] ,[ArXiv preprint].

Publications:

  1. "Discrete-time inference for slow-fast systems driven by fractional Brownian motion", (with Solesne Bourguin and Siragan Gailus), 2021, SIAM Journal on Multiscale Modeling and Simulation, [ArXiv preprint], to appear.
  2. "How reaction-diffusion PDEs approximate the large-population limit of stochastic particle models", (with Samuel A. Isaacson and Jingwei Ma), 2021, SIAM Journal on Applied Mathematics, [ArXiv preprint], to appear.
  3. "Normalization effects on shallow neural networks and related asymptotic expansions", (with Jiahui Yu), 2021, AIMS Journal on Foundations of Data Science , [ArXiv preprint], to appear.
  4. "Asymptotics of Reinforcement Learning with Neural Networks", (with Justin Sirignano), 2021, Stochastic Systems, [ArXiv preprint], to appear.
  5. "Metastability and exit problems for systems of stochastic reaction-diffusion equations", (with Michael Salins), 2021, Annals of Probability ,[ArXiv preprint], to appear.
  6. "Mean field analysis of deep neural networks", (with Justin Sirignano), 2020, Mathematics of Operations Research, [ArXiv preprint], to appear.
  7. "Typical dynamics and fluctuation analysis of slow-fast systems driven by fractional Brownian motion", (with Solesne Bourguin and Siragan Gailus), 2020, Stochastics and Dynamics, [ArXiv preprint], to appear.
  8. "Optimal investment and derivative demand under price impact", (with Michail Anthropelos and Scott Robertson), 2020, Mathematical Finance, [ArXiv preprint], to appear.
  9. "Selection of quasi-stationary states in the stochastically forced Navier-Stokes equation on the torus", (with Margaret Beck, Eric Cooper and Gabriel Lord), 2020, Journal of Nonlinear Science , Volume 30, pp. 1677–1702, [ArXiv preprint].
  10. "Network effects and default clustering for large systems", (with Jia Yang), 2020, Journal of Applied Mathematical Finance, Volume 26, Issue 6, pp. 523-582, [ArXiv preprint].
  11. "Importance sampling for slow-fast diffusions based on moderate deviations", (with Matthew Morse), 2020, SIAM Journal on Multiscale Modeling and Simulation, Vol. 18, No. 1, pp. 315--350. [ArXiv preprint].
  12. "Mean field analysis of neural networks: a law of large numbers", (with Justin Sirignano), 2020, SIAM Journal on Applied Mathematics, Vol. 80, Issue 2, pp. 725--752. [ArXiv preprint].
  13. "Information geometry for approximate Bayesian computation", 2020, SIAM/ASA Journal on Uncertainty Quantification, Vol. 8, Issue 1, pp. 229--260 [ArXiv preprint].
  14. "Optimal scaling of the MALA algorithm with irreversible proposals for Gaussian targets", (with Michela Ottobre and Natesh S. Pillai), 2020, Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 8, pp. 311--361 [ArXiv preprint]
  15. "Stochastic gradient descent in continuous time: a central limit theorem", (with Justin Sirignano), 2019, Stochastic Systems , Volume 10, Issue 2, pp. 99-191, [ArXiv preprint].
  16. "Mean field analysis of neural networks: A central limit theorem", (with Justin Sirignano), 2020, Stochastic Processes and their Applications , Volume 130, Issue 3, March 2020, pp. 1820-1852, [ArXiv preprint].
  17. "Pathwise moderate deviations for option pricing", (with Antoine Jacquier), 2019, Mathematical Finance, Vol. 30, Issue 2, pp. 426--463, [ArXiv preprint].
  18. "Large deviations and averaging for systems of slow--fast stochastic reaction--diffusion equations", (with Wenqing Hu and Michael Salins), 2019, Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 7, Issue 4, pp. 808-?874, [ArXiv preprint].
  19. "Selection of quasi-stationary states in the Navier-Stokes equation on the torus", (with Margaret Beck and Eric Cooper), 2019, Nonlinearity , Vol. 32, pp. 209--237, [ArXiv preprint].
  20. "Analysis of multiscale integrators for multiple attractors and irreversible Langevin samplers", (with Jianfeng Lu), 2018, SIAM Multiscale Modeling and simulation , Vol. 16, Issue 4, pp. 1859--1883. [ArXiv preprint].
  21. "Discrete-time statistical inference for multiscale diffusions", (with Siragan Gailus), 2018, SIAM Multiscale Modeling and simulation , Vol. 16, Issue 4, pp. 1824--1858, [ArXiv preprint].
  22. "DGM: A deep learning algorithm for solving partial differential equations", (with Justin Sirignano), 2018, Journal of Computational Physics , Vol. 375, pp. 1339--1364, [ArXiv preprint].
  23. "Sequential Monte Carlo for fractional Stochastic Volatility Models", (with Alexandra Chronopoulou), 2018, Quantitative Finance , Vol. 18, Issue 3, pp. 507--517, [ArXiv preprint].
  24. "Indifference pricing for Contingent Claims: Large Deviations Effects", (with Scott Robertson), 2018, Mathematical Finance , Vol. 28, Issue 1, pp. 335--371, [ArXiv preprint].
  25. "Stochastic gradient descent in continuous time", (with Justin Sirignano), 2017, SIAM Journal on Financial Mathematics, Vol. 8, Issue 1, pp. 933--961, [ArXiv preprint]
  26. "Dimension Reduction in Statistical Estimation of Partially Observed Multiscale Processes", (with Andrew Papanicolaou), 2017, SIAM Journal on Uncertainty Quantification, Vol. 5, pp. 1220-1247, [ArXiv preprint]
  27. "Hypoelliptic multiscale Langevin diffusions: Large deviations, invariant measures and small mass asymptotics", (with Wenqing Hu), 2017, Electronic Journal of Probability, Vol. 22 (2017), paper no. 55, pp. 1-38, [ArXiv preprint]
  28. "Rare event simulation via importance sampling for linear SPDE's", (with Michael Salins), 2017, Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 5, Issue 4, pp. 652-690, [ArXiv preprint].
  29. "The effect of heterogeneity on flocking behavior and systemic risk", (with Fei Fang and Yiwei Sun), 2017, Statistics and Risk Modelling, Vol. 34, No. 3--4, pp. 141-155, [ArXiv preprint]
  30. "Moderate deviations principle for systems of slow-fast diffusions", (with Matthew R. Morse), 2017, Asymptotic Analysis, Vol. 105, No. 3-4, pp. 97-135, [ArXiv preprint].
  31. "The pricing of contingent claims and optimal positions in asymptotically complete markets", (with Michail Anthropelos and Scott Robertson), 2017, Annals of Applied Probability, , Vol. 27, No. 3, pp. 1778-1830, [ArXiv preprint]
  32. "Markov processes with spatial delay: path space characterization, occupation time and properties", (with Michael Salins), 2017, Stochastics and Dynamics , Vol. 17, No. 6, 1750042 (21 pages), [ArXiv preprint].
  33. "Statistical Inference for Perturbed Multiscale Dynamical Systems", (with Siragan Gailus), 2017, Stochastic Processes and their Applications , Volume 127, Issue 2, pp. 419-448, [ArXiv preprint]
  34. "Improving the convergence of reversible samplers", (with Luc Rey-Bellet), 2016, Journal of Statistical Physics , August 2016, Vol. 164, Issue 3, pp. 472-494, [ArXiv preprint].
  35. "Rare event simulation for multiscale diffusions in random environments", 2015, SIAM Multiscale Modeling and Simulation , Vol. 13, No. 4, pp. 1290--1311 [ArXiv preprint].
  36. "Escaping from an Attractor: Importance Sampling and Rest Points I", (with Paul Dupuis and Xiang Zhou), 2015, Annals of Applied Probability , Vol. 25, No. 5, pp. 2909-2958, [ArXiv preprint]
  37. "Irreversible Langevin samplers and variance reduction: a large deviation approach", (with Luc Rey-Bellet), 2015, Nonlinearity , Vol. 28, pp. 2081-2103, [ArXiv preprint]
  38. "Default Clustering in Large Pools: Large Deviations", (with Richard Sowers), 2015, SIAM Journal on Financial Mathematics , Vol. 6, (2015), pp. 86-116, [SSRN], [ArXiv preprint].
  39. "Quenched Large Deviations for Multiscale Diffusion Processes in Random Environments", 2015, Electronic Journal of Probability, Vol. 20, (2015), no. 15, pp. 1-29, [ArXiv preprint]
  40. "Variance reduction for irreversible Langevin samplers and diffusion on graphs", (with Luc Rey-Bellet), 2015, Electronic Communications in Probability, Vol. 20, (2015), no. 15, pp. 1-16, [ArXiv preprint].
  41. "Non-asymptotic performance analysis of importance sampling schemes for small noise diffusions", 2015, Journal of Applied Probability , Vol. 52, pp. 1-14, [ArXiv preprint]
  42. "Large Portfolio Asymptotics for Losses from Default", (with Kay Giesecke, Richard Sowers and Justin A. Sirignano), 2015, Mathematical Finance, Vol. 25, No. 1, (January 2015), pp. 77-114, [SSRN] ,[ArXiv preprint]
  43. "Rare event simulation in the neighborhood of a rest point", (with Paul Dupuis), 2014, Winter Simulation Conference, article in pdf , (IEEE, 2014), pp. 564-573 .
  44. "Filtering the Maximum Likelihood for Multiscale Problems", (with Andrew Papanicolaou), 2014, SIAM Multiscale Modeling and Simulation , Vol. 12, No. 3, pp. 1193-1229, [ArXiv preprint].
  45. "Fluctuations Analysis for Loss from Default", (with Kay Giesecke and Justin A. Sirignano), 2014, Stochastic Processes and their Applications, Volume 124, Issue 7, pp. 2322-2362, [SSRN],[ArXiv preprint].
  46. "Scaling Limits and Exit Law for Multiscale Diffusions", (with Sergio A. Almada), 2014, Asymptotic Analysis, Volume 87, pp. 65-90, [ArXiv preprint].
  47. "Fluctuation analysis and short time asymptotics for multiple scales diffusion processes", 2014, Stochastics and Dynamics, Vol. 14, No.3, pp. 1350026 [ArXiv preprint].
  48. "Maximum likelihood estimation for small noise multiscale disffusions", (with Alexandra Chronopoulou), 2013, Statistical Inference for Stochastic Processes,Volume 16, Issue 3, pp. 237-266, [ArXiv preprint]
  49. "Large Deviations and Importance Sampling for Systems of Slow-Fast Motion", 2013, Applied Mathematics and Optimization, Vol. 67, pp. 123-161, [ArXiv preprint]
  50. "Default Clustering in Large Portfolios: Typical Events", (with Kay Giesecke and Richard Sowers), 2013, Annals of Applied Probability, Volume 23, Number 1, pp. 348-385, [SSRN], [ArXiv preprint].
  51. "Importance Sampling for Multiscale Diffusions", (with Paul Dupuis and Hui Wang), 2012, SIAM Multiscale Modeling and Simulation , Vol. 12, No. 1, pp. 1-27, [ArXiv preprint].
  52. "Large Deviations for Multiscale Diffusions via Weak Convergence Methods", (with Paul Dupuis), 2012, Stochastic Processes and Their Applications, 122, pp. 1947-1987, [ArXiv preprint].
  53. "Large Deviations Principle for a Large Class of One-Dimensional Homogeneous Strong Markov Processes", 2012, Journal of Theoretical Probability, Volume 25, Issue 4, pp. 925-949, [ArXiv preprint]
  54. "Recovery Rates in Investment-Grade Pools of Credit Assets: A Large Deviations Analysis", (with Richard Sowers), 2011, Stochastic Processes and Their Applications, Volume 121, Issue 12, pp. 2861-2898, [SSRN] ,[ArXiv preprint].
  55. "Rare Event Simulation in Rough Energy Landscapes", (with Paul Dupuis and Hui Wang), 2011, Winter Simulation Conference, article in pdf , (IEEE, 2011), pp. 504-515.
  56. "Wiener Process with Reflection in Nonsmooth Narrow Tubes", 2009, Electronic Journal of Probability, Vol. 14, Paper no. 69, pp. 2011-2037 article in pdf
  57. "Method of Moments Estimation of Ornstein-Uhlenbeck Processes Driven by General Levy Process", 2009, Annales de l'I.S.U.P., Volume 53 - Fascicule 2-3, pp. 3-19 [ArXiv preprint]
  58. "Reaction Diffusion Equations with Non-Linear Boundary Conditions in Narrow Domains", (with Mark Freidlin), 2008, Asymptotic Analysis, Volume 59, Number 3-4, pp.227-249 article in pdf
  59. "A note on the Smoluchowski- Kramers approximation for the Langevin equation with reflection", 2007, Stochastics and Dynamics, Vol. 7, No. 2, pp. 141-153 : article in pdf

Other Publications:

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Distinctions, Awards and Grants:

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Editorial Work:

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Invited Talks and Lectures:

Workshops and Conferences that I have attended:

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Seminars that I have co-organized or I am co-organizing:

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Graduate Teaching:

Undergraduate Teaching:

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